Mathematical and Physical Papers, Volume 1

Cover......Page 1
Frontmatter......Page 6
PREFACE......Page 10
Contents......Page 14
On the Steady Motion of Incompressible Fluids......Page 16
On some cases of Fluid Motion......Page 32
On the Motion of a Piston and of the Air in a Cylinder......Page 84
On the Theories of the Internal Friction of Fluids in Motion, and of the Equilibrium and Motion of Elastic Solids......Page 90
SECTION I.--Explanation of the Theory of Fluid Motion proposed. Formation of the Differential Equations. Application of these Equations to a few simple eases......Page 93
SECTION II. -- Objections to Lagrange\'s proof of the theorem that if udx+vdy + wdz is an exact differential at any one instant it is always so, the pressure being supposed equal in all directions. Principles of M. Cauchy\'s proof. A new proof of the theorem. A physical interpretation of the circumstance of the above expression being an exact differential......Page 121
SECTION III.--Application of a method analogous to that of Section I. to the determination of the equations of equilibrium and motion of elastic solids......Page 128
SECTION IV.--Principles of Poisson\'s theory of elastic solids, and of the oblique pressures existing in fluids in motion. Objections to one of his hypotheses. Reflections on the constitution, and equations of motion of the luminiferous ether in vacuum......Page 131
On the Proof of the Proposition that (Mx + Ny)-1 is an Integrating Factor of the Homogeneous Differential Equation M+N dy/dx = 0......Page 145
On the Aberration of Light......Page 149
On Fresnel\'s Theory of the Aberration of Light......Page 156
On a Formula for determining the Optical Constants of Doubly Refracting Crystals......Page 163
On the Constitution of the Luminiferous Ether, viewed with reference to the Aberration of Light......Page 168
Report on Recent Researches on Hydrodynamics......Page 172
I. General theorems connected with the ordinary equations of Fluid Motion......Page 173
II. Theory of waves, including tides......Page 176
III. The discharge of gases through small orifices......Page 191
IV. Theory of sound......Page 193
V. Simultaneous oscillations of fluids and solids......Page 194
VI. Formation of the equations of motion when the pressure is not supposed equal in all directions......Page 197
Supplement to a Memoir on some cases of Fluid Motion......Page 203
On the Theory of Oscillatory Waves......Page 212
On the Resistance of a Fluid to two Oscillating Spheres......Page 245
On the Critical Values of the Sums of Periodic Series......Page 251
SECTION I. --Mode of ascertaining the nature of the discontinuity of a function which is expanded in a series of sines or cosines, and of obtaining the developments of the derived functions......Page 254
SECTION II. ---Mode of ascertaining the nature of the discontinuity of the integrals which are analogous to the series considered in Section I., and of obtaining the developments of the derivatives of the expanded functions......Page 286
SECTION III.--On the discontinuity of the sums of infinite series, and of the values of integrals taken between infinite limits......Page 294
SECTION IV.--Examples of the application of the formulas proved in the preceding sections......Page 301
Supplement to a paper on the Theory of Oscillatory Waves......Page 329
Index......Page 342